Problem: The sum of two numbers is $99$, and their difference is $25$. What are the two numbers?
Solution: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 99}$ ${x-y = 25}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 124 $ $ x = \dfrac{124}{2} $ ${x = 62}$ Now that you know ${x = 62}$ , plug it back into $ {x+y = 99}$ to find $y$ ${(62)}{ + y = 99}$ ${y = 37}$ You can also plug ${x = 62}$ into $ {x-y = 25}$ and get the same answer for $y$ ${(62)}{ - y = 25}$ ${y = 37}$ Therefore, the larger number is $62$, and the smaller number is $37$.